Elementary arithmetic, with brief notices of its history... by Robert Potts.

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11. 2 days' work of A = 3 days' work of C;
and 5 days' work of B = 4 days' work of C.. 8 days' work of A = 12 days' work of C;
and 15 days' work of B= 12 days' work of C.
Hence 8 days' work of = 15 days' work of B,
and 1 day's work of A =_- 1 days' work of B.
Therefore 36 days' work of = 15x36 or 67~ days' work of B,
8
or B will require 67~ days to complete what A can perform in 6 weeks.
12. 3~ days. 13. 3-1 days. 14. 5 days.
XXXI.
1. 1728 cubic inches =1000 ounces Avoirdupois. loz. water -lb. = 70~ ~ grains.
Hence 1 cubic inch of water = Io -~ X 1 = 252 grains Troy. 2. 4j- cubic yards..
3. Content of the cistern 56 X 31 X 27=14x31 3 cubic feet.
334
1 cubic foot of water=lO1000oz. = - 1000- of ton.
16x 112x 20'
Therefore weight of water= 1x 10 _0 31X32 232 = 36 - tons,
16X112X20 8X8 64
the pressure on the bottom of the cistern, which is at the rate 527- tons on the
square foot.
4. 3402 hogsheads. 5. 120 gallons.
6. Glass A contains 3 parts water + 1 part spirits = 4 parts.
Glass B contains 4 parts water + 3 parts spirit = 7 parts.
i of water +- 1 of spirit =1,
and 7 of water + A of spirit = 1,
therefore 1-29 of water+ of spirit =2.
Or the mixture consists of 1-9- of water, and 28 of spirit.
7. The first vessel contains I1. gallons, the second 22- gallons. 8. 7945 -ounces. 9. 21151bs. on the square foot, and nine times this pressure on the square
yard. 10. 32661bs. 11. 1716- feet.
XXXII.
1. 8 hour. 2. 84 minutes. 3. 60 minutes. 4. 7 full.
5. The capacity of the cistern may be represented by 1. Pipe A fills the cistern
in 3 hours, and pours in ~ in 1 hour. Pipe B fills it in 4 hours, and pours in 1 ii.
1 hour. The pipes A and B pour in ~+4 or -17 in 1 hour; but pipe C empties the
cistern or pours out 1 in 1 hour. Hence the quantity poured out being greater than
the quantity porured i~n during the same time, the cistern will become empty in a
certain time. At 3 o'clock, when pipe C is opened, the cistern contains 3+ 4 or I-1.
And in 1 hour, 1l-. -~=1 is excess of quantity poured out above that poured in.
Hence 1 ~-~-T_=-%=2- hours. The vessel will be empty 27 hours after 3 o'clock, or
at 12 minutes past 5 o'clock.
6. -'of a day.
7. I anm a brazen lion, with fountains in my two eyes, my mouth, and in my
right foot. The water flowing from my right eye fills a reservoir in two days, and
from the left in three, and from the foot in four. But when the water flows from my
mouth, it fills the reservoir in six hours. In what time will the reservoir be filled
by the water from the mouth, the eyes, and the foot, if all be opened together?
In 37- hours the reservoir will be filled.
XXXIII.
1. The difference is 1760X31829 X minutes, or more than 1, but less thal
1- of a minute.